Basic Circuit Theory

Preface
1 - Lumped Circuits and Kirchhoff's Laws
	1 - Lumped Circuits
	2 - Reference Directions
	3 - Kirchhoff's Current Law (KCL)
	4 - Kirchhoff's Voltage Law (KVL)
	5 - Wavelength and Dimension of the Circuit
2 - Circuit Elements
	1 - Resistors
		1.1 - The Linear Time-invariant Resistor
		1.2 - The Linear Time-varying Resistor
		1.3 - The Nonlinear Resistor
	2 - Independent Sources
		2.1 - Voltage Source
		2.2 - Current Source
		2.3 - Thévenin and Norton Equivalent Circuits
		2.4 - Waveforms and Their Notation
		2.5 - Some Typical Waveforms
	3 - Capacitors
		3.1 - The Linear Time-invariant Capacitor
		3.2 - The Linear Time-varying Capacitor
		3.3 - The Nonlinear Capacitor
	4 - Inductors
		4.1 - The Linear Time-invariant Inductor
		4.2 - The Linear Time-varying Inductor
		4.3 - The Nonlinear Inductor
		4.4 - Hysteresis
	5 - Summary of Two-terminal Elements
	6 - Power and Energy
		6.1 - Power Entering a Resistor, Passivity
		6.2 - Energy Stored in Time-invariant Capacitors
		6.3 - Energy Stored in Time-invariant Inductors
	7 - Physical Components versus Circuit Elements
3 - Simple Circuits
	1 - Series Connection of Resistors
	2 - Parallel Connection of Resistors
	3 - Series and Parallel Connection of Resistors
	4 - Small-signal Analysis
	5 - Circuits with Capacitors or Inductors
		5.1 - Series Connection of Capacitors
		5.2 - Parallel Connection of Capacitors
		5.3 - Series Connection of Inductors
		5.4 - Parallel Connection of Inductors
4 - First-order Circuits
	1 - Linear Time-invariant First-order Circuit, Zero-input Response
		1.1 - The RC (Resistor-Capacitor) Circuit
		1.2 - The RL (Resistor-Inductor) Circuit
		1.3 - The Zero-input Response as a Function of the Initial State
		1.4 - Mechanical Example
	2 - Zero-state Response
		2.1 - Constant Current Input
		2.2 - Sinusoidal Input
	3 - Complete Response: Transient and Steady-state
		3.1 - Complete Response
		3.2 - Transient and Steady State
		3.3 - Circuits with Two Time Constants
	4 - The Linearity of the Zero-state Response
	5 - Linearity and Time Invariance
		5.1 - Step Response
		5.2 - The Time-invariance Property
		5.3 - The Shift Operator
	6 - Impulse Response
	7 - Step and Impulse Responses for Simple Circuits
	8 - Time-varying Circuits and Nonlinear Circuits
5 - Second-order Circuits
	1 - Linear Time-invariant RLC Circuit, Zero-input Response
	2 - Linear Time-invariant RLC Circuit, Zero-state Response
		2.1 - Step Response
		2.2 - Impulse Response
	3 - The State-space Approach
		3.1 - State Equations and Trajectory
		3.2 - Matrix Representation
		3.3 - Approximate Method for the Calculation of the Trajectory
		3.4 - State Equations and Complete Response
	4 - Oscillation, Negative Resistance, and Stability
	5 - Nonlinear and Time-varying Circuits
	6 - Dual and Analog Circuits
		6.1 - Duality
		6.2 - Mechanical and Electrical Analog
6 - Introduction to Linear Time-invariant Circuits
	1 - Some General and Properties
	2 - Node and Mesh Analyses
		2.1 - Node Analysis
		2.2 - Mesh Analysis
	3 - Input-Output Representation (nth-order Differential Equation)
		3.1 - Zero-input Response
		3.2 - Zero-state Response
		3.3 - Impulse Response
	4 - Response to an Arbitrary Input
		4.1 - Derivation of the Convolution Integral
		4.2 - Example of a Convolution Integral in Physics
		4.3 - Comments on Linear Time-varying Circuits
		4.4 - The Complete Response
	5 - Computation of Convolution Integrals
7 - Sinusoidal Steady-state Analysis
	1 - Review of Complex Numbers
		1.1 - Description of Complex Numbers
		1.2 - Operations with Complex Numbers
	2 - Phasors and Ordinary Differential Equations
		2.1 - The Representation of a Sinusoid by a Phasor
		2.2 - Application of the Phasor Method to Differential Equations
	3 - Complete Response and Sinusoidal Steady-state Response
		3.1 - Complete Response
		3.2 - Sinusoidal Steady-state Response
		3.3 - Superposition in the Steady State
	4 - Concepts of Impedance and Admittance
		4.1 - Phasor Relations for Circuit Elements
		4.2 - Definition of Impedance and Admittance
	5 - Sinusoidal Steady-state Analysis of Simple Circuits
		5.1 - Series-Parallel Connections
		5.2 - Node and Mesh Analyses in the Sinusoidal Steady State
	6 - Resonant Circuits
		6.1 - Impedance, Admittance, and Phasors
		6.2 - Network Function, Frequency Response
	7 - Power in Sinusoidal Steady State
		7.1 - Instantaneous, Average, and Complex Power
		7.2 - Additive Property of Average Power
		7.3 - Effective or Root-Mean-Square Values
		7.4 - Theorem on the Maximum Power Transfer
		7.5 - Q of a Resonant Circuit
	8 - Impedance and Frequency Normalization
8 - Coupling Elements and Coupled Circuits
	1 - Coupled Inductors
		1.1 - Characterization of Linear Time-invariant Coupled Inductors
		1.2 - Coefficient of Coupling
		1.3 - Multiwinding Inductors and Their Inductance Matrix
		1.4 - Series and Parallel Connections of Coupled Inductors
		1.5 - Double-tuned Circuits
	2 - Ideal Transformers
		2.1 - Two-winding Ideal Transformer
		2.2 - Impedance-changing Properties
	3 - Controlled Sources
		3.1 - Characterization of Four Kinds of Controlled Source
		3.2 - Examples of Circuit Analysis
		3.3 - Other Properties of Controlled Sources
9 - Network Graphs and Tellegen's Theorem
	1 - The Concept of a Graph
	2 - Cut Sets and Kirchhoff's Current Law
	3 - Loops and Kirchhoff's Voltage Law
	4 - Tellegen's Theorem
	5 - Applications
		5.1 - Conservation of Energy
		5.2 - Conservation of Complex Power
		5.3 - The Real Part and Phase of Driving-point Impedances
		5.4 - Driving Point Impedance, Power Dissipated, and Energy Stored
10 - Node and Mesh Analyses
	1 - Source Transformations
	2 - Two Basic Facts of Node Analysis
		2.1 - Implications of KCL
		2.2 - Implications of KVL
	3 - Tellegen's Theorem Revisited
	4 - Node Analysis of Linear Time-invariant Networks
		3.1 - Analysis of Resistive Networks
		3.2 - Writing Node Equations by Inspection
		3.3 - Sinusoidal Steady-state Analysis
		3.4 - Integrodifferential Equations
		3.5 - Shortcut Method
	4 - Duality
		4.1 - Planar Graphs, Meshes, Outer Meshes
		4.2 - Dual Graphs
		4.3 - Dual Networks
	5 - Two Basic Facts of Mesh Analysis
		5.1 - Implications of KVL
		5.2 - Implications of KCL
	6 - Mesh Analisys of Linear Time-invariant Networks
		6.1 - Sinusoidal Steady-state Analisys
		6.2 - Integrodifferential Equations
11 - Loop and Cut-set Analisys
	1 - Fundamental Theorem of Graph Theory
	2 - Loop Analysis
		2.1 - Two Basic Facts
		2.2 - Loop Analysis for Linear Time-invariant Networks
		2.3 - Properties of the Loop Impedance Matrix
	3 - Cut-set Analysis
		3.1 - Two Basic Facts of Cut-set Analysis
		3.2 - Cut-set Analysis for Linear Time-invariant Networks
		3.3 - Properties of the Cut-set Admittance Matrix
	4 - Comments on Loop and Cut-set Analysis
	5 - Relation Between B and Q
12 - State Equations
	1 - Linear Time-invariant Networks
	2 - The Concept of State
	3 - Nonlinear and Time-varying Networks
		3.1 - Linear Time-varying Case
		3.2 - Nonlinear Case
	4 - State Equations for Linear Time-invariant Networks
13 - Laplace Transforms
	1 - Definition of the Laplace Transform
	2 - Basic Properties of the Laplace Transform
		2.1 - Uniqueness
		2.2 - Linearity
		2.3 - Differentiation Rule
		2.4 - Integration Rule
	3 - Solutions of Simple Circuits
		3.1 - Calculation of an Impulse Response
		3.2 - Partial-fraction Expansion
		3.3 - Zero-state Response
		3.4 - The Convolution Theorem
		3.5 - The Complete Response
	4 - Solution of General Networks
		4.1 - Formulation of Linear Algebraic Equations
		4.2 - The Cofactor Method
		4.3 - Networks Functions and Sinusoidal Steady State
	5 - Fundamental Properties of Linear Time-invariant Networks
	6 - State Equations
	7 - Degerate Networks
	8 - Sufficient Conditions for Uniqueness
14 - Natural Frequencies
	1 - Natural Frequency of a Network Variable
	2 - The Elimination Method
		2.1 - General Remarks
		2.2 - Equivalent Systems
		2.3 - The Elimination Algorithm
		2.4 - Natural Frequencies of a Network
		2.5 - Natural Frequencies and State Equations
15 - Network Functions
	1 - Definition, Examples, and General Property
	2 - Poles, Zeros and Frequency Response
	3 - Poles, Zeros and Impulse Response
	4 - Physical Interpretation of Poles and Zeros
		4.1 - Poles
		4.2 - Natural Frequencies of a Network
		4.3 - Zeros
	5 - Application to Oscillator Design
	6 - Symmetry Properties
16 - Network Theorems
	1 - The Substitution Theorem
		1.1 - Theorem, Examples, and Application
		1.2 - Proof of the Substitution Theorem
	2 - The Superposition Theorem
		2.1 - Theorem, Remarks, Examples, and Corollaries
		2.2 - Proof of the Superposition Theorem
	3 - Thévenin-Norton Equivalent Network Theorem
		3.1 - Theorem, Examples, Remarks, and Corollary
		3.2 - Special Cases
		3.3 - Proof of Thévenin Theorem
		3.4 - An Application of the Thévenin Equivalent Network Theorem
	4 - The Reciprocity Theorem
		4.1 - Theorem, Examples, and Remarks
		4.2 - Proof of the Reciprocity Theorem
17 - Two-ports
	1 - Review of One-ports
	2 - Resistive Ports
		2.1 - Various Two-port Descriptions
		2.2 - Terminated Nonlinear Two-ports
		2.3 - Incremental Model and Small-signal Analysis
	3 - Transistor Examples
		3.1 - Common-base Configuration
		3.2 - Common-emitter Configuration
	4 - Coupled Inductors
	5 - Impedance and Admittance Matrices of Two-ports
		5.1 - The (Open-circuit) Impedance Matrix
		5.2 - The (Short-circuit) Admittance Matrix
		5.3 - A Terminated Two-port
	6 - Other Two-port Parameter Matrices
		6.1 - The Hybrid Matrices
		6.2 - The Transmission Matrices
18 - Resistive Networks
	1 - Physical Networks and Networks Models
	2 - Analysis of Resistive Networks from a Power Point of View
		2.1 - Linear Networks Made of Passive Resistors
		2.2 - Minimum Property of Dissipated Power
		2.3 - Minimizing Appropiate Functions
		2.4 - Nonlinear Resistive Networks
	3 - The Voltage Gain and the Current Gain of a Resistive Network
		3.1 - Volage Gain
		3.2 - Current Gain
19 - Energy and Passivity
	1 - Linear Time-varying Capacitor
		1.1 - Description of the Circuit
		1.2 - Pumping Energy into the Circuit
		1.3 - State-space Interpretation
		1.4 - Energy Balance
	2 - Energy Stored in Nonlinear Time-varying Elements
		2.1 - Energy Stored in a Nonlinear Time-varying Inductor
		2.2 - Energy Balance in a Nonlinear Time-varying Inductor
	3 - Passive One-ports
		3.1 - Resistors
		3.2 - Inductors and Capacitors
		3.3 - Passive One-ports
	4 - Exponential Input and Exponential Response
	5 - One-ports Made of Passive Linear Time-invariant Elements
	6 - Stability of Passive Networks
		6.1 - Passive Networks and Stable Networks
		6.2 - Passivity and Stability
		6.3 - Passivity and Network Functions
	7 - Parametric Amplifier
Appendix A: Functions and Linearity
	1 - Functions
		1.1 - Introduction to the Concept of Function
		1.2 - Formal Definition
	2 - Linear Functions
		2.1 - Scalars
		2.2 - Linear Spaces
		2.3 - Linear Functions
Appendix B: Matrices and Determinants
	1 - Matrices
		1.1 - Definition
		1.2 - Operations
		1.3 - More Definitions
		1.4 - The Algebra of nxn Matrices
	2 - Determinants
		2.1 - Definitions
		2.2 - Properties of Determinants
		2.3 - Cramer's Rule
		2.4 - Determinant Inequalities
	3 - Linear Dependence and Rank
		3.1 - Linear Independent Vectors
		3.2 - Rank of a Matrix
		3.3 - Linear Independent Equations
	4 - Positive Definite Matrix
Appendix C: Differential Equations
	1 - Linear Equation of Order n
		1.1 - Definitions
		1.2 - Properties Based on Linearity
		1.3 - Existence and Uniqueness
	2 - The Homogeneous Linear Equation with Constant Coefficients
		2.1 - Distinct Characteristic Roots
		2.2 - Multiple Characteristic Roots
	3 - Paricular Solutions of L(D)y(t)=b(t)
	4 - Nonlinear Differential Equations
		4.1 - Interpretation of the Equation
		4.2 - Existence and Uniqueness
Index